As long as you're not talking about the entry stuff, 2eq, then they have both. Where Denon is better is that the selectability according to any specific listening mode is normally/always there, but not so with Onkyo. Stereo, with AS engaged in Onkyo can't really be had as flat (though there's a pretty nutty workaround), and if you're in THX mode for example, there really isn't the "Audyssey House Curve", but the Flat curve with THX Re-Eq applied. It will never apply both Reeq AND the Audyssey curve simultaneously, so no fear of a very steep rolloff. One can simply turn off the re-eq to have the flat curve as flat. While even very knowledgeable posters mistakenly point out something similar to what you've said, I would agree that implementation can sometimes be better. By far, most rooms are not significantly treated, and in such cases I think the AS curve would be desired.
I find your subjective opinion about music playback with this tech quite interesting, thanks. I've never had this tech, and so I'm curious. If it was me, and I actually had AS for my stereo, I'm pretty certain I'd be using the flat curve, but who knows.
OTOH, I do think most people using dyn eq/vol are doing so with movies as the top priority, if only for dialogue intelligibility, with much less fear of waking the kids, or angering the neighbors. Not quite as much need for that with music, IMO.